The 27-year-old faces an uncertain future with Tottenham, following a series of disparaging remarks made towards his club, and Ben Davies is arguably now considered to be Mauricio Pochettino's first-choice left sided defender.
Liverpool, meanwhile, are in need of a top class left-back, with Alberto Moreno currently Jürgen Klopp's only recognised left-sided full-back.
James Milner can fill in when required, but if the Merseysiders are going to mount a sustained challenge for major honours over the course of the next few years, they will surely need to strengthen that position.
SkyBET, though, believe it could be a very real possibility, and list Liverpool as 7/1 outsiders in the race for the England international's signature, behind Manchester United, who are the 11/2 favourites.
The 27-year-old full-back would be a sensational signing for Klopp's side, but it is debatable whether the German has the funds to tempt Spurs into selling, having already laid out £75 million on bringing Virgil van Dijk to the club.
With the January window now open, this will certainly be one for both Liverpool and Tottenham fans to keep a close eye on.